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Angles (geometric), normalization and conversion: Difference between revisions

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Angles (geometric), normalization and conversion (view source)

Revision as of 01:56, 1 November 2021

190 bytes removed ,  2 years ago
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The solution of this seemingly trivial task could be elegantly done by type classes. Each angle unit is represented as a distinct type, preventing from implicit combination of different units. Moreover, adding new units doesn't imply writing new transformers or normalizers.
 
Isomorphims between all angular types are defined via representation of fullas turns, according to the fact that they all form the same topological space, isomorphic to '''S'''¹open ≃interval [0(-1, 1).
 
<lang haskell>{-# LANGUAGE RankNTypes #-}
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instance Show Rad where
show (Rad r) = printf "∠ ∠%.3f" r
instance Angle Rad where
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instance Show Grad where
show (Grad g) = printf "%.3gg" . valueg
instance Angle Grad where
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λ> angle pi :: Rad
∠ 3∠3.141
 
λ> angle 1000 :: Gon
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λ> (from :: Gon -> Rad) 100
∠ 1∠1.571
 
λ> (from :: Rad -> Gon) $ (pi/2)
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<pre>λ> main
converting to radians
[∠ ∠-2.000,∠ ∠-1.000,∠ 0∠0.000,∠ 1∠1.000,∠ 2∠2.000,∠ 6∠6.283,∠ 3∠3.434,∠ 0∠0.747,∠ 0∠0.858,∠ 3∠3.159,∠ 2∠2.717,∠ 5∠5.926]
[∠ ∠-0.035,∠ ∠-0.017,∠ 0∠0.000,∠ 0∠0.017,∠ 0∠0.035,∠ 0∠0.110,∠ 0∠0.279,∠ 1∠1.000,∠ 6∠6.266,∠ 0∠0.681,∠ 4∠4.869,∠ 4∠4.887]
[∠ ∠-0.031,∠ ∠-0.016,∠ 0∠0.000,∠ 0∠0.016,∠ 0∠0.031,∠ 0∠0.099,∠ 0∠0.251,∠ 0∠0.900,∠ 5∠5.639,∠ 6∠6.267,∠ 6∠6.267,∠ 0∠0.000]
[∠ ∠-0.002,∠ ∠-0.001,∠ 0∠0.000,∠ 0∠0.001,∠ 0∠0.002,∠ 0∠0.006,∠ 0∠0.016,∠ 0∠0.056,∠ 0∠0.352,∠ 0∠0.392,∠ 6∠6.282,∠ 1∠1.571]
[∠ ∠-1.107,∠ ∠-0.785,∠ 0∠0.000,∠ 0∠0.785,∠ 1∠1.107,∠ 1∠1.413,∠ 1∠1.508,∠ 1∠1.553,∠ 1∠1.568,∠ 1∠1.568,∠ 1∠1.571,∠ 1∠1.571]
 
converting to degrees
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